Eur. Phys. J. B (2018) 91: 65
https://doi.org/10.1140/epjb/e2018-80630-y

Regular Article

Chimera states in networks of logistic maps with hierarchical connectivities

Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany

^a e-mail: omelchenko@itp.tu-berlin.de

Received: 4 November 2017
Received in final form: 19 December 2017
Published online: 6 April 2018

Abstract

Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilution of the network links influences the appearance of chimera patterns. The network connectivities are constructed using an iterative Cantor algorithm to generate fractal (hierarchical) connectivities. Increasing the hierarchical level of iteration, we compare the resulting spatiotemporal patterns. We demonstrate that a high clustering coefficient and symmetry of the base pattern promotes chimera states, and asymmetric connectivities result in complex nested chimera patterns.